erwin a. mart´ı-paname...

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Generacion Pulsada en Laseres de Fibra Optica

Erwin A. Martı-Panameno

Facultad de Ciencias Fısico-MatematicasBenemerita Universidad Autonoma de Puebla

Mexico

San Jose, Costa Rica, 9 de Mayo, 2012

Erwin A. Martı-Panameno (BUAP)Generacion Pulsada en Laseres de Fibra Optica

1San Jose, Costa Rica, 9 de Mayo, 2012 1

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Plan de la Presentacion

.. .1 Introduccion: Regımenes de Generacion Pulsados

Pulsos Luminosos

.. .2 Q–Switching

Mecanismos de Modulacion de Q.

.. .3 Amarre de Modos

Descripcion Temporal del Amarre de ModosAmarre de Modos en Laseres de Fibra Optica

.. .4 Conclusiones



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Un laser de fibra optica dopada con iones de elementos de TierrasRaras, es una buena fuente de radiacion optica. Puede ser explotadaen otras aplicaciones mas avanzadas como la generacion de pulsosluminosos cortos y ultracortos.Mediante multiples estadios de amplificacion se pueden obtenerpotencias pico del orden de los GW y duraciones femtosegundo.



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Pulsos Luminosos

Un pulso luminoso u optico es un destello de radiacionelectromagnetica, que se caracteriza entre otras cosas por:

...1 Duracion temporal τ0

...2 Forma del Pulso

...3 Potencia Pico

...4 Energıa portada

...5 Fase . . .etc.



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Duracion Temporal τ0

Existen varias formas de definirla, la mas comun es a partir del anchotemporal total de la mitad de la intensidad pico.Conocido como duracion FWHM.Son comunes en optica pulsos en los rangos de nanosegundo afemtosegundo.



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Forma del Pulso

Representacion grafica de la perturbacion luminosa en funcion deltiempo.Las formas mas tıpicas son:

Gaussiana

sech2

HipergaussianaLorentziana . . .etc.



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Forma del Pulso


Gaussianasech2




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Forma del Pulso


Gaussianasech2

Hipergaussiana

Lorentziana . . .etc.



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Forma del Pulso


Gaussianasech2




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Potencia Pico

Una de las grandes ventajas de trabajar con pulsos luminosos es laposibilidad de alcanzar potencias pico desde los Kilowatts hastaTerawatts:

PP = ffEp

τ0

ff = 0,94 y 0,88 para pulsos gaussianos y sech, respectivamente.

Ep = 1mJ y τ0 = 10fs producen:

PP ∼ 100MW



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Potencia Pico

Una de las grandes ventajas de trabajar con pulsos luminosos es laposibilidad de alcanzar potencias pico desde los Kilowatts hastaTerawatts:

PP = ffEp

τ0

ff = 0,94 y 0,88 para pulsos gaussianos y sech, respectivamente.Ep = 1mJ y τ0 = 10fs producen:

PP ∼ 100MW



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Potencia Pico

Potencias de cientos de GW e incluso TW se obtienen a partir desistemas de amplificacion.

Alternativa para energıa limpia: Fusion Nuclear Controlada por laserhttp://www.hiper-laser.org



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Potencia Pico

Potencias de cientos de GW e incluso TW se obtienen a partir desistemas de amplificacion.Alternativa para energıa limpia: Fusion Nuclear Controlada por laserhttp://www.hiper-laser.org



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Pulsos Limitados por Transformada de Fourier

Un pulso Limitado por Transformada de Fourier (LTF) es aquel cuyoproducto duracion por ancho de banda es mınimo. Concepto aplicadoa pulsos no chispeados.

Pulso Gaussiano: ∆ν · τ0 ≈ 0,44

Pulso Sech: ∆ν · τ0 ≈ 0,32



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Detengamonos en las tecnicas de generacion de Pulsos LuminososCortos.Nos centraremos en dos tecnicas fundamentales y diferentes en suoperacion:

Q-Switching o regimen de pulsos gigantes. Ep ∼ mJ − J yτ0 ∼ µs− ns.Mode Locking o Amarre de Modos: Ep < µJ y τ0 ∼ ps− fs.



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Q-Switching o regimen de pulsos gigantes. Ep ∼ mJ − J yτ0 ∼ µs− ns.

Mode Locking o Amarre de Modos: Ep < µJ y τ0 ∼ ps− fs.



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Q-Switching o regimen de pulsos gigantes. Ep ∼ mJ − J yτ0 ∼ µs− ns.Mode Locking o Amarre de Modos: Ep < µJ y τ0 ∼ ps− fs.



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El regimen de Q–switching encuentra multiples aplicaciones. En laindustria como un elemento para cortar y grabar materiales. Enmedicina para operaciones de desprendimiento de retina. Endermatologıa, para remediar imperfecciones de la piel, removertatuajes, etc.



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Factor de Calidad de una Cavidad Laser: Q

Uno de los parametros mas relevantes en la caracterizacion deldesempe no de laseres se da a partir de la cavidad laser. Comocircuito oscilatorio, su calidad se evalua a partir del factor-Q:

Q =Energıa Almacenada

Energıa perdida por ciclo

Esta expresion puede llevarse a:



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Q =Frecuencia central

Ancho de banda FWHM de la cavidadEs decir:

Q =ν

2δνc

Donde (para una cavidad FP):

δνc =1

4π

[c

2Lln

(1

r1r2

)]



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Si Q es grande la cavidad presenta bajas perdidas yconsecuentemente estamos ante mejores condiciones para el laseo.Haciendo

Q = Q(t)

Podemos crear condiciones para que el medio activo almaceneenergıa y despues sacarla del laser en un tiempo corto.



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Diagrama esquematico de un laser Modulado en Q

Figura: Laser en regimen Q-switch



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Figura: Dinamica entre Ganancia y Perdidas en un laser Modulado en Q



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Al interior de la cavidad se inserta un elemento bloqueando la emisionestimulada, a la vez que el bombeo se mantiene. Esto permite que elmedio activo acumule energıa. Ante una subita

Espejo rotante.

Switches electroopticos.Switches Acustoopticos.Absorvedores saturables.



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Espejo rotante.Switches electroopticos.

Switches Acustoopticos.Absorvedores saturables.



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Espejo rotante.Switches electroopticos.Switches Acustoopticos.

Absorvedores saturables.



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Espejo rotante.Switches electroopticos.Switches Acustoopticos.Absorvedores saturables.



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Q–Switching

Algunos parametros:

Laseres de estado solido, duraciones de decenas de ns,intensidades pico de GW, decenas de J.

Laser todo fibra (Er): Potencias pico decenas de KW.τ ∼ 50ns− 1µs. Energıa 1J 1

1A.S. Kurkov, Laser Phys. Lett. V 8, N 5, p.335, (2011)



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Es posible generar pulsos de duraciones menores a las obtenidasmediante Q-switch, e intensidades pico mayores. Diferencia envarios ordenes de magnitud.Laser en Amarre de Modo



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Introduccion

Con esta tecnica es posible generar pulsos opticos en el lımite teorico:

τ0 ∼ T0

donde T0 es el perıodo de oscilacion de la frecuencia portadora.

Necesitamos laseres con un gran numero de modos longitudinales.



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Introduccion

En general los Modos Electromagneticos, no estan ligados unos aotros. Sus relaciones de fase son aleatorias. Sabemos que lacondicion de resonancia de la cavidad impone la relacion a laslongitudes de onda a emitirse

λn =2L

n

donde n es un numero muy grande. λn debe estar contenidos bajo lalınea de emision del medio activo.



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Introduccion

Si los logramos poner los modos en fase, tendremos un regimen degeneracion completamente nuevo: el amarre de modos ( o ModeLocking), el cual permite la generacion de pulsos luminosos de muycorta duracion y, bajo determinadas condiciones, de altasintensidades.

A diferencia del Q–Switching, en Amarre de Modos forzamos laspropiedades de generacion del laser. Q–Switching puede alcanzarseen laseres de un solo modo, mientras que Amarre de Modos esindispensable la operacion multimodal.



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Introduccion

Si los logramos poner los modos en fase, tendremos un regimen degeneracion completamente nuevo: el amarre de modos ( o ModeLocking), el cual permite la generacion de pulsos luminosos de muycorta duracion y, bajo determinadas condiciones, de altasintensidades.A diferencia del Q–Switching, en Amarre de Modos forzamos laspropiedades de generacion del laser.

Q–Switching puede alcanzarseen laseres de un solo modo, mientras que Amarre de Modos esindispensable la operacion multimodal.



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Introduccion

Si los logramos poner los modos en fase, tendremos un regimen degeneracion completamente nuevo: el amarre de modos ( o ModeLocking), el cual permite la generacion de pulsos luminosos de muycorta duracion y, bajo determinadas condiciones, de altasintensidades.A diferencia del Q–Switching, en Amarre de Modos forzamos laspropiedades de generacion del laser. Q–Switching puede alcanzarseen laseres de un solo modo, mientras que Amarre de Modos esindispensable la operacion multimodal.



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Descripcion Temporal del Amarre de Modos

Consideremos que el laser emite N modos longitudinales, cada unocon su frecuencia ωl e igualmente espaciados ∆ω , de igual fase yamplitud. Cada modo puede ser caracterizado por:

xl(t) = x0 sin (ωnt+ ϕ0) = Imx0 exp i(ωnt+ ϕ0)

dondeωl = ω0 + l∆ω

l = −N − 1

2,−N − 1

2+ 1,−N − 1

2+ 2, · · · , N − 1

2



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La suma:

X(t) =∑l

xl(t) = x0Im

(∑l

exp i(ω0 + ϕ0 + l∆ωt)

)

o bien

X(t) = x0Im

(exp i(ω0t+ ϕ0)

∑l

exp (il∆ωt)

)donde ω0 – frecuencia central.



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Empleemos la identidad general:

(N−1)/2∑−(N−1)/2

eily =sin (Ny/2)

(y/2)

de donde,

X(t) = x0 sin (ω0t+ ϕ0)sin (N∆ωt/2)

sin (∆ωt/2)

X(t) = An(t) sin (ω0t+ ϕ0)

conAn(t) = x0

sin (N∆ωt/2)

sin (∆ωt/2)



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An(t) = x0sin (N∆ωt/2)sin (∆ωt/2)

Since sin x is the imaginary part of eix, we may write this as

X(t) ! x0ImX

n

ei(v0t"f0"nDt)

!

! x0Im ei(v0t"f0)X

n

einDt !

: (6:7:4)

The general identity

X(N#1)=2

#(N#1)=2

einy ! sin (Ny=2)sin (y=2)

(6:7:5)

proved below allows us to write (6.7.4) as

X(t) ! x0Im ei(v0t"f0)sin(NDt=2)sin(Dt=2)

! "! x0 sin(v0t " f0)

sin(NDt=2)sin(Dt=2)

! "

! AN(t)x0 sin(v0t " f0): (6:7:6)

The function AN(t) is plotted in Fig. 6.7 for N ! 3 and N ! 7. In general AN(t) hasequal maxima

AN(t)max ! N (6:7:7)

– –(N –1)!12

+ –(N –1)!12–! +!0

w0

Figure 6.6 A collection of N frequencies running from v0 # 12 (N # 1)D to v0 " 1

2 (N # 1)D as inEq. (6.7.2).

7.0

3.5

0

AN

(t)

–3.5

–1 0 1 2

!t p —

3 4 5

N = 3

N = 7—t7 = — ! p

2 7

Figure 6.7 The function AN (t) ! sin 12NDt# $

=sin 12Dt# $

vs. Dt/p.

240 MULTIMODE AND PULSED LASING

Figura: Laser en regimen Q-switch. Esta figura se va a cambiar por unasimulacion en clase empleando mathematica. Esta fig es tomada de Milonni



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Para lograr el Amarre de Modos necesitamos, de alguna forma,interactuar con los modos longitudinales.Se deben poner todos en fase, para lo que se introducira unmodulador.El perıodo de modulacion es el tiempo que tarda la luz en dar unavuelta completa a la cavidad:

Tm = 2Lopt/c



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Existen diversos mecanismos para lograr el amarre de modos.Aquı solo indicaremos algunos:

Amarre de Modos ActivoAmplitudFase

Amarre de Modos Pasivo.

Absorvedores saturables ultra-rapidos.Mecanismos de Auto Amarre de modos: KLM, Espejos no lineales,etc.



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Amarre de Modos Activo

AmplitudFase





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Amarre de Modos ActivoAmplitud

Fase





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Absorvedores saturables ultra-rapidos.

Mecanismos de Auto Amarre de modos: KLM, Espejos no lineales,etc.



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Amarre de Modos en Laseres de Fibra Optica

Figura: Laser en regimen de FO con un modulador de Amplitud



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Los LFO son muy versatiles para lograr el amarre de modos.Espejos no lineales de Lazo.Laser de Fibra de doble nucleo.etc. . . .

Analizaremos brevemente los dos primeros.



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Laseres de Fibra con espejo de lazo

April 15,1991 / Vol. 16, No. 8 / OPTICS LETTERS 539

All-fiber ring soliton laser mode locked with a nonlinear mirror

Irl N. Duling IIINaval Research Laboratory, Washington, D.C. 20375

Received December 6, 1990; accepted February 7, 1991

An amplifying nonlinear-optical fiber loop mirror is used as the gain element in an all-fiber ring laser. The resultingdouble-loop structure resembles a figure eight. The output of the amplifying nonlinear-optical fiber loop mirror isfed back to the input through an optical isolator to ensure unidirectional operation. The laser produces 2-pstransform-limited pulses. The pulse energy corresponds to that of the fundamental soliton in the fiber used.

The introduction of Er-doped fibers for amplificationin optical communication systems has led to the possi-bility of long-distance, high-speed soliton-based com-munication in the second transmission window of theoptical fibers. A source for this wavelength range thatprovides short pulses (preferably solitons), at highrepetition rates and at a wavelength compatible withthe Er amplifiers, has yet to be identified. A fewcandidates have been suggested, but in all cases activemodulation is required to initiate pulse formation.l-4This Letter describes a self-starting all-fiber laser thatproduces solitons by passive mode locking of a fiberring with a nonlinear amplifying loop mirror (NALM)that contains an Er-doped fiber. This laser producestransform-limited pulses as short as 2 ps, at averagepowers of as much as 3 mW and a wavelength of 1.535,um.

The idea of mode locking a laser with a nonlinearfiber mirror has been proposed5 and demonstrated6

for a linear laser that uses either a bulk-optic or fiberreflector at the other end of an amplifying segment,but no short-pulse generation has been demonstrated.In addition, polarization controllers are necessary toprovide a -r linear phase offset of the loop mirror,which precludes the use of polarization-preserving fi-ber. Here the author presents a ring laser modelocked by a NALM, so that no active mode locking isnecessary in the laser and no polarization control isnecessary if the laser is built from polarization-pre-serving fiber.

The configuration of the system is shown in Fig. 1.The laser consists of a NALM with its output connect-ed to its input. The resulting shape of the laser sug-gested the name of figure-eight laser (F8L). The F8Lcan be considered as an external loop that consists of apolarization-independent isolator, a 20% output cou-pler, and a polarization controller and an internal loopthat contains the Er-doped fiber, an appropriatepump coupler [a wavelength-division multiplexer(WDM)], a length of fiber, and a polarization control-ler. The WDM was designed to couple all the 980-nmpump light into the internal loop while allowing noneof the 1.5-Am light to leak out.

The internal loop operates as a NALM, which hasbeen described by Fermann et al.7 The high-intensityportions of a pulse will be preferentially transmitted

through the mirror, while the low-intensity portionsare reflected into the original fiber. This operation issimilar to that found in a nonlinear-optical loop mir-ror8 (NOLM), where the imbalance in counterpropa-gating pulse intensities is due to a mirror coupler thatis not exactly 50%. The NALM, however, has a signif-icantly lower switching threshold than the NOLM9 aswell as inherent gain.7 The Er-doped fiber was 2 m inlength, provided 80% pump absorption, and had adoping concentration of 400 parts in 106 and a corediameter of 5 ,m.

The concept of operation of the F8L is that as apulse propagates around the external loop it is short-ened and amplified by each transmission through theNALM. The high-intensity portions of the pulse aretransmitted and amplified, while the low-intensityportions are reflected and rejected by the optical isola-tor. The isolator is crucial in this configuration, as itprovides a mechanism to eliminate this unwantedlight from the cavity. If the average dispersion for oneround trip is of the proper sign, solitonlike pulses canform in the laser. It has been demonstrated by Blowet al. that solitons will be transmitted through aNOLM with no change in pulse shape and nearly unittransmission.10 Since the laser has no active modula-tion, it can produce pulses at any repetition rate de-sired that is an integer multiple of the cavity round-trip time. Pulse separations corresponding to repeti-tion rates from 3 MHz to 71 GHz have been observed

polarization

opticalisolator

Er

/1.535 Am 980 nm

Fig. 1. Configuration of the figure-eight laser. The loop offiber in the nonlinear mirror was varied from 90 to 2 m.

0146-9592/91/080539-03$5.00/0

April 15,1991 / Vol. 16, No. 8 / OPTICS LETTERS 539

All-fiber ring soliton laser mode locked with a nonlinear mirror

Irl N. Duling IIINaval Research Laboratory, Washington, D.C. 20375

Received December 6, 1990; accepted February 7, 1991

An amplifying nonlinear-optical fiber loop mirror is used as the gain element in an all-fiber ring laser. The resultingdouble-loop structure resembles a figure eight. The output of the amplifying nonlinear-optical fiber loop mirror isfed back to the input through an optical isolator to ensure unidirectional operation. The laser produces 2-pstransform-limited pulses. The pulse energy corresponds to that of the fundamental soliton in the fiber used.

The introduction of Er-doped fibers for amplificationin optical communication systems has led to the possi-bility of long-distance, high-speed soliton-based com-munication in the second transmission window of theoptical fibers. A source for this wavelength range thatprovides short pulses (preferably solitons), at highrepetition rates and at a wavelength compatible withthe Er amplifiers, has yet to be identified. A fewcandidates have been suggested, but in all cases activemodulation is required to initiate pulse formation.l-4This Letter describes a self-starting all-fiber laser thatproduces solitons by passive mode locking of a fiberring with a nonlinear amplifying loop mirror (NALM)that contains an Er-doped fiber. This laser producestransform-limited pulses as short as 2 ps, at averagepowers of as much as 3 mW and a wavelength of 1.535,um.

The idea of mode locking a laser with a nonlinearfiber mirror has been proposed5 and demonstrated6

for a linear laser that uses either a bulk-optic or fiberreflector at the other end of an amplifying segment,but no short-pulse generation has been demonstrated.In addition, polarization controllers are necessary toprovide a -r linear phase offset of the loop mirror,which precludes the use of polarization-preserving fi-ber. Here the author presents a ring laser modelocked by a NALM, so that no active mode locking isnecessary in the laser and no polarization control isnecessary if the laser is built from polarization-pre-serving fiber.

The configuration of the system is shown in Fig. 1.The laser consists of a NALM with its output connect-ed to its input. The resulting shape of the laser sug-gested the name of figure-eight laser (F8L). The F8Lcan be considered as an external loop that consists of apolarization-independent isolator, a 20% output cou-pler, and a polarization controller and an internal loopthat contains the Er-doped fiber, an appropriatepump coupler [a wavelength-division multiplexer(WDM)], a length of fiber, and a polarization control-ler. The WDM was designed to couple all the 980-nmpump light into the internal loop while allowing noneof the 1.5-Am light to leak out.

The internal loop operates as a NALM, which hasbeen described by Fermann et al.7 The high-intensityportions of a pulse will be preferentially transmitted

through the mirror, while the low-intensity portionsare reflected into the original fiber. This operation issimilar to that found in a nonlinear-optical loop mir-ror8 (NOLM), where the imbalance in counterpropa-gating pulse intensities is due to a mirror coupler thatis not exactly 50%. The NALM, however, has a signif-icantly lower switching threshold than the NOLM9 aswell as inherent gain.7 The Er-doped fiber was 2 m inlength, provided 80% pump absorption, and had adoping concentration of 400 parts in 106 and a corediameter of 5 ,m.

The concept of operation of the F8L is that as apulse propagates around the external loop it is short-ened and amplified by each transmission through theNALM. The high-intensity portions of the pulse aretransmitted and amplified, while the low-intensityportions are reflected and rejected by the optical isola-tor. The isolator is crucial in this configuration, as itprovides a mechanism to eliminate this unwantedlight from the cavity. If the average dispersion for oneround trip is of the proper sign, solitonlike pulses canform in the laser. It has been demonstrated by Blowet al. that solitons will be transmitted through aNOLM with no change in pulse shape and nearly unittransmission.10 Since the laser has no active modula-tion, it can produce pulses at any repetition rate de-sired that is an integer multiple of the cavity round-trip time. Pulse separations corresponding to repeti-tion rates from 3 MHz to 71 GHz have been observed

polarization

opticalisolator

Er

/1.535 Am 980 nm

Fig. 1. Configuration of the figure-eight laser. The loop offiber in the nonlinear mirror was varied from 90 to 2 m.

0146-9592/91/080539-03$5.00/0

Figura: Artıculo OriginalErwin A. Martı-Panameno (BUAP)Generacion Pulsada en Laseres de Fibra Optica


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Laseres de Fibra con espejo de lazo

540 OPTICS LETTERS / Vol. 16, No. 8 / April 15,1991

1.1

c5

Pg

0.9

0.7

0.5

0.3

0.1

-0.1

70

60

50

40

30

20

10

0

-35 -25 -15 -5 5 15 25 35Time Delay (ps)

1533 1534 1535 1536 1537 1538

Wavelength (nm)Fig. 2. (a) Autocorrelation and (b) the spectrum of the laseroutput, with AVAr = 0.32.

from the F8L, indicating that indeed there is no limi-tation to the repetition rate beyond those of pulseenergy and power extraction from the Er gain fiber.

The polarization controllers are put in the loops forcompensation of the stress birefringence of the fiber.Since the optical isolator is polarization independent,there is no strong polarization selection in the cavity.The controllers then serve to define the particularpolarization eigenstate of the light in the cavity. Inaddition, the controller in the loop mirror can be usedto provide a linear phase shift between the counter-propagating beams. If polarization-preserving fiberswere used to construct the F8L, no polarization con-trollers would be needed, since the polarization statewould be well defined and the linear phase differentialin the loop would be properly set to zero.

Three different loop lengths were examined to de-termine the optimum length. The first was 55 m ofdispersion-shifted fiber (IDI = 0.43 ps/nm-km at 1.535am). This fiber did not support solitons, but the laserproduced 4-ps pulses at 3 MHz with AvAP- = 0.81. Thesecond fiber was 30 m of standard telecommunicationsfiber (IDI = 16 ps/nm-km at 1.535,um). Figure 2 showsthe autocorrelation of the pulse and its optical spec-trum. This fiber produced pulses of 2.1-ps durationat 5.5 MHz with AvAr = 0.32 (close to the theoreticaltime-bandwidth product for a hyperbolic-secant-

shaped pulse of 0.3148). By variation of the orienta-tion of the polarization controllers, the average powerin the laser could be decreased, while the pulse dura-tion was observed to lengthen with a correspondingnarrowing of the spectrum, which could be evidence ofsoliton formation.

Since solitons are transmitted through the nonlin-ear mirror with the least loss, it is expected that theoperating point of the F8L is reached when the peakpower of the soliton corresponds to the switching pow-er of the NALM. The equation

Ps = AeffX/n2L(g - 1) (1)

gives the switching power of the NALM, where n2 isthe nonlinear index, L is the length of the fiber, Aeff isthe effective fiber area, and g is the optical gain.7 Theequation defining the soliton peak power is

Pi = (.776X 3) IDIAeff (2)

where P1 is the peak power, IDI is the fiber dispersion,X is the signal wavelength, and T is the pulse width.1Combining Eq. (2) with Eq. (1) leads one to

(2 = (.776x 2 IDIL(g - 1), (3)

which indicates that since the gain (g) in the steadystate is fixed by the cavity loss, the pulse width can bereduced by shortening the fiber loop or lowering thefiber dispersion. It is interesting to note that thenonlinear index and the effective area are also missingfrom this equation, so in this picture the operatingpoint is not determined by these characteristics of thefiber. For our experimental conditions, IDI = 16 ps/nm-km, Aeff = 8.66 X 10-11 m2 , n2 = 3.2 X 10-20, and r= 2.1 ps, which lead to Pi = 29.5 W. This value agreeswell with the experimentally determined value of 31 Wfor the circulating peak power with the 30-m loop.

An important consideration in passively mode-locked lasers is whether they are able to self-start.That is, can the laser build pulses on its own, or does itrequire an outside noise source to initiate pulsing,which then becomes self-sustaining? In the case ofthe F8L, the result of low-intensity operation of theNALM is to reflect all light and frustrate lasing. Inthat case it would be expected that the laser would notbe self-starting. If, however, a small amount of linearleakage is permitted, either by allowing the coupler tobe different from 50% or by inserting a small amountof relative phase shift in the ring, the resulting cwlasing will carry enough noise to initiate pulsing. Theself-starting behavior in our laser was observed forpump powers above 80 mW (absorbed), although puls-ing could be obtained with as little as 50 mW of power.It should be noted that although these powers arerelatively high, the efficiency of our fiber is low (esti-mated at 0.5 dB/mW). If a more efficient fiber wereused (2-5 dB/mW), then the same gain could be ob-tained with a currently available diode laser as thepump.

40

-40)

a)I'd

540 OPTICS LETTERS / Vol. 16, No. 8 / April 15,1991

1.1

c5

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0

-35 -25 -15 -5 5 15 25 35Time Delay (ps)

1533 1534 1535 1536 1537 1538

Wavelength (nm)Fig. 2. (a) Autocorrelation and (b) the spectrum of the laseroutput, with AVAr = 0.32.

from the F8L, indicating that indeed there is no limi-tation to the repetition rate beyond those of pulseenergy and power extraction from the Er gain fiber.

The polarization controllers are put in the loops forcompensation of the stress birefringence of the fiber.Since the optical isolator is polarization independent,there is no strong polarization selection in the cavity.The controllers then serve to define the particularpolarization eigenstate of the light in the cavity. Inaddition, the controller in the loop mirror can be usedto provide a linear phase shift between the counter-propagating beams. If polarization-preserving fiberswere used to construct the F8L, no polarization con-trollers would be needed, since the polarization statewould be well defined and the linear phase differentialin the loop would be properly set to zero.

Three different loop lengths were examined to de-termine the optimum length. The first was 55 m ofdispersion-shifted fiber (IDI = 0.43 ps/nm-km at 1.535am). This fiber did not support solitons, but the laserproduced 4-ps pulses at 3 MHz with AvAP- = 0.81. Thesecond fiber was 30 m of standard telecommunicationsfiber (IDI = 16 ps/nm-km at 1.535,um). Figure 2 showsthe autocorrelation of the pulse and its optical spec-trum. This fiber produced pulses of 2.1-ps durationat 5.5 MHz with AvAr = 0.32 (close to the theoreticaltime-bandwidth product for a hyperbolic-secant-

shaped pulse of 0.3148). By variation of the orienta-tion of the polarization controllers, the average powerin the laser could be decreased, while the pulse dura-tion was observed to lengthen with a correspondingnarrowing of the spectrum, which could be evidence ofsoliton formation.

Since solitons are transmitted through the nonlin-ear mirror with the least loss, it is expected that theoperating point of the F8L is reached when the peakpower of the soliton corresponds to the switching pow-er of the NALM. The equation

Ps = AeffX/n2L(g - 1) (1)

gives the switching power of the NALM, where n2 isthe nonlinear index, L is the length of the fiber, Aeff isthe effective fiber area, and g is the optical gain.7 Theequation defining the soliton peak power is

Pi = (.776X 3) IDIAeff (2)

where P1 is the peak power, IDI is the fiber dispersion,X is the signal wavelength, and T is the pulse width.1Combining Eq. (2) with Eq. (1) leads one to

(2 = (.776x 2 IDIL(g - 1), (3)

which indicates that since the gain (g) in the steadystate is fixed by the cavity loss, the pulse width can bereduced by shortening the fiber loop or lowering thefiber dispersion. It is interesting to note that thenonlinear index and the effective area are also missingfrom this equation, so in this picture the operatingpoint is not determined by these characteristics of thefiber. For our experimental conditions, IDI = 16 ps/nm-km, Aeff = 8.66 X 10-11 m2 , n2 = 3.2 X 10-20, and r= 2.1 ps, which lead to Pi = 29.5 W. This value agreeswell with the experimentally determined value of 31 Wfor the circulating peak power with the 30-m loop.

An important consideration in passively mode-locked lasers is whether they are able to self-start.That is, can the laser build pulses on its own, or does itrequire an outside noise source to initiate pulsing,which then becomes self-sustaining? In the case ofthe F8L, the result of low-intensity operation of theNALM is to reflect all light and frustrate lasing. Inthat case it would be expected that the laser would notbe self-starting. If, however, a small amount of linearleakage is permitted, either by allowing the coupler tobe different from 50% or by inserting a small amountof relative phase shift in the ring, the resulting cwlasing will carry enough noise to initiate pulsing. Theself-starting behavior in our laser was observed forpump powers above 80 mW (absorbed), although puls-ing could be obtained with as little as 50 mW of power.It should be noted that although these powers arerelatively high, the efficiency of our fiber is low (esti-mated at 0.5 dB/mW). If a more efficient fiber wereused (2-5 dB/mW), then the same gain could be ob-tained with a currently available diode laser as thepump.

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Figura: Pulsos y espectro generados



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Laser de Fibra de doble nucleo

Figura: Seccion Transversal de la fibra de doble nucleoErwin A. Martı-Panameno (BUAP)

Generacion Pulsada en Laseres de Fibra Optica33

San Jose, Costa Rica, 9 de Mayo, 2012 33/ 36 .

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Figura: Proceso auto-amarre de modos y formacion de solitones



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Conclusiones

Hemos discutido una de las propiedades mas importantes como es lade generar pulsos de corta duracion y alta intensidad. Nos centramosen las principales metodos de trabajo de laseres pulsados:Q-Switching y Amarre de Modos.Analizamos la versatilidad de los laseres de fibra optica paraamarrarse en modos.



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erwin a. mart´ı-paname...

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